Answer:
[tex]xy^{\frac{2}{9}}[/tex] = [tex]x\sqrt[9]{y^2}[/tex]
Explanation:
Given
[tex]xy^{\frac{2}{9}}[/tex]
Required
Write an equivalent expression
[tex]xy^{\frac{2}{9}}[/tex]
Split the expression
[tex]x * y^{\frac{2}{9}}[/tex]
Further, simplify using the following law of indices: [tex]a^{ \frac{m}{n}} = a^{ m * \frac{1}{n}}[/tex]
[tex]x * y^{\frac{2}{9}}[/tex] becomes
[tex]x * y^{2 * \frac{1}{9}}[/tex]
This in turn gives:
[tex]x * (y^{2}) ^{* { \frac{1}{9}}}[/tex]
In indices: [tex]y^{\frac{1}{n}} = \sqrt[n] y[/tex]
[tex]x * (y^{2}) ^{* { \frac{1}{9}}}[/tex] becomes
[tex]x * \sqrt[9]{ y^2}[/tex]
[tex]x\sqrt[9]{y^2}[/tex]
Hence:
[tex]xy^{\frac{2}{9}}[/tex] = [tex]x\sqrt[9]{y^2}[/tex]
